Coatings Technology Handbook Episode 1 Part 2 pot

2 -4 Coatings Technology Handbook, Third Edition of coating rheology. If meaningful correlations are to be made with coating phenomena, the viscosity must be measured over a wide range of strain rates. The most acceptable technique for determining the strain-rate dependence of the viscosity is the use of the constant rate-of-strain experiment in torsion. This can be done in either a cone-and-plate (for low rates) or a concentric cylinder geometry (for higher rates). However, the oscillatory, or dynamic measurement, is also commonly employed for the same purpose. It is assumed that the shear strain rate and the frequency are equivalent quantities, and the complex viscosity is equal to the steady state constant rate viscosity (i.e., the Cox–Merz rule is valid). The applicability of the Cox–Merz rule, however, is by no means universal, and its validity must be demonstrated before the dynamic measurements can be substituted for the steady-state ones. The capillary technique, as employed in several commercial instru- ments, is not suitable for coating studies in general, because it is more suitable for measuring viscosity at higher strain rates. 2.2.3 Thixotropy Thixotropy is a much abused term in the coatings industry. In the review, we shall define the phenomenon of thixotropy as the particular case of the time dependence of the viscosity, that is, its decrease during a constant rate-of-strain experiment. This time dependence manifests itself in hysteresis in experiments involving increasing and decreasing rates of strain. The area under the hysteresis loop has been used as a quantitative estimate of thixotropy, although its validity is still a matter of debate. 18,19 Another attempt at quantifying thixotropy 20 involves the measurement of a peak stress ( σ p ) and a stress at a long time ( σ ∞ ) in a constant rate-of-strain experiment. In this instance, the thixotropy index β is defined as follows: (2.4) The utility of these different definitions is still unclear, and their correlation to coating phenomena is even less certain. In a purely phenomenological sense, thixotropy can be studied by monitoring the time-dependence of the viscosity, at constant rates of strain. Quantification of the property is, however, rather arbitrary. The coefficient of thixotropy, β , appears to be the most reasonable, and is measurable in torsional TA B LE 2.2 Some Commercially Available Rheological Instrumentation Name of Instrument Geometries Available Shear-Rate Range Modes Available We issenberg Rheogoniometer Couette, cone and plate, parallel plate Broad Steady shear, oscillatory Rheometrics Mechanical Spectrometer Couette, plate and cone, parallel plate Broad Steady shear, oscillatory Carri-Med Controlled Stress Rheometer (CSR) Couette, parallel plate Fixed stress Creep and recovery, oscillatory Rheo-Tech Viscoelastic Rheometer (VER) Cone and plate Fixed stress Oscillatory, creep and recovery Contraves Rheomat 115 Cone and plate, couette Broad Steady shear Rheometrics Stress Rheometer Cone and plate Fixed stress Oscillatory, creep and recovery Haake Rotovisco Couette, cone and plate Broad Steady state Shirley-Ferranti Cone and plate Broad Steady shear ICI Rotothinner Couette Single high rate Steady shear Brookfield Cone and Plate Cone and plate Medium to high Steady Brookfield Spindle Undefined Undefined Steady shear Gardner-Holdt Rising bubble Undefined Cannon-Ubbelohde Poiseuille Limited range, high end Shear Brushometer Couette High end only, single Steady shear βσ σ σ =− ∞ p p DK4036_book.fm Page 4 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC Coating Rheology 2 -5 increases with increase in the rate of strain. In addition, the thixotropic behavior is influenced consid- erably by the shear history of the material. In comparative measurements, care should be taken to ensure a similar or identical history for all samples. The phenomenon of thixotropy is also responsible for the viscosity is monitored using a sinusoidal technique, it will be found to increase to a value characteristic of a low shear rate-of-strain measurement. 2.2.4 Dilatancy The original definition of dilatancy, 21 an increase in viscosity with increasing rate of strain, is still the most widely accepted one today. 22–24 The term has been used, however, to mean the opposite of thixot- ropy. 25 The constant rate-of-strain experiment, outlined above for viscosity measurements, can obviously be employed to determine shear thickening, or dilatancy 2.2.5 Yield Stress In the case of fluids, the yield stress is defined as the minimum shear stress required to initiate flow. It is also commonly referred to as the “Bingham stress,” and a material that exhibits a yield stress is commonly known as a “Bingham plastic” or viscoplastic. 26 Though easily defined, this quantity is not as easily measured. Its importance in coating phenomena is, however, quite widely accepted. The most direct method of measuring this stress is by creep experiments in shear. This can be accomplished in the so-called stress-controlled rheometers (see Table 2.2). The minimum stress that can be imposed on a sample varies with the type of instrument, but by the judicious use of geometry, stress (in shear) in the range of 1 to 5 dynes/cm 2 can be applied. This is the range of yield stresses exhibited by most paints with a low level of solids. However, the detection of flow is not straightforward. In the conventional sense, the measured strain in the sample must attain linearity in time when permanent flow occurs. This may necessitate the measurement over a long period of time. An estimate of the yield stress may be obtained from constant rate-of-strain measurements of stress and viscosity. When the viscosity is plotted against stress, its magnitude appears to approach infinity at low stresses. The asymptote on the stress axis gives an estimate of the yield stress. Another method used is the stress relaxation measurement after the imposition of a step strain. For materials exhibiting viscoplasticity, the stress decays to a nonzero value that is taken as the estimate of the yield stress. 2.2.6 Elasticity Elasticity of coating materials is frequently mentioned in the literature 18,19 as being very important in determining the coating quality, particularly of leveling. However, most of the reported measurements of elasticity are indirect, either through the first normal stress difference or through the stress relaxation measurement. Correlations are shown to exist, in paints, between high values of the first normal stress difference and the leveling ability. 18 However, no satisfactory rationalization has been put forward for a cause-and-effect relationship. Also, direct measurement of the elasticity of a coating through the creep- and-recovery experiment is virtually nonexistent. We shall not discuss the role of elasticity in this chapter. 2.3 Rheological Phenomena in Coating Coalescence, wetting, leveling, cratering, sagging, and slumping are the processes that are strongly influenced by surface tension and viscoelasticity. These, in turn, are the two important parameters that control the quality and appearance of coatings, and hence, their effects on the coating process are discussed in detail. DK4036_book.fm Page 5 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC increase in viscosity after the cessation of shear. If after a constant rate-of strain experiment, the material rheometers such as those mentioned in Table 2.2. It should be noted that this index, as defined above, 2 -6 Coatings Technology Handbook, Third Edition 2.3.1 Wetting Surface tension is an important factor that determines the ability of a coating to wet and adhere to a substrate. The ability of a paint to wet a substrate has been shown to be improved by using solvents with lower surface tensions. 27 Wetting may be quantitatively defined by reference to a liquid drop resting in equilibrium on a solid surface (Figure 2.4). The smaller the contact angle, the better the wetting. When θ is greater than zero, the liquid wets the solid completely over the surface at a rate depending on a liquid viscosity and the solid surface roughness. The equilibrium contact angle for a liquid drop sitting an ideally smooth, homogeneous, flat, and nondeformable surface is related to various interfacial tensions by Young’s equation: (2.5) where γ lv is the surface tension of the liquid in equilibrium with its own saturated vapor, γ sv is the surface tension of the solid in equilibrium with the saturated vapor of the liquid, and γ sl is the interfacial tension between the solid and liquid. When θ is zero and assuming γ sv to be approximately equal to γ s (which is usually a reasonable approximation), then from Equation 2.5, it can be concluded that for spontaneous wetting to occur, the surface tension of the liquid must be greater than the surface tension of the solid. It is also possible for the liquid to spread and wet a solid surface when θ is greater than zero, but this requires the application of a force to the liquid. 2.3.2 Coalescence Coalescence is the fusing of molten particles to form a continuous film. It is the first step in powder coating. The factors that control coalescence are surface tension, radius of curvature, and viscosity of the Dodge 28 related the time of coalescence to those factors by the equation, (2.6) where t c is the coalescence time and R c is the radius of the curvature (the mean particle radius). To minimize the coalescence time such that more time is available for the leveling-out stage, low viscosity, small particles, and low surface tension are desirable. 2.3.3 Sagging and Slumping Sagging and slumping are phenomena that occur in coatings applied to inclined surfaces, in particular, to vertical surfaces. Under the influence of gravity, downward flow occurs and leads to sagging or slumping, depending on the nature of the coating fluid. In the case of purely Newtonian or shear thinning the other hand, a material with a yield stress exhibits slumping (plug flow and shear flow). FIGURE 2.4 Schematic illustration of good and poor wetting. γ lv γ sv γ sl Solid Liquid Vapor θ Better Good Poor γθγγ lv sv sl cos =− tf R c c =       η γ DK4036_book.fm Page 6 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC molten powder. Figure 2.5 shows a schematic diagram of the coalescence of molten powder. Nix and fluids, sagging (shear flow) occurs; Figure 2.6 represents “gravity-induced” flow on a vertical surface. On 2 -8 Coatings Technology Handbook, Third Edition as well as a time factor t , which is really a time interval for which the material remains fluid (or the time the material takes to solidify). The velocity v 0 depends inversely on the zero-shear viscosity. When all other things are equal, a shear thinning fluid ( n < 1) will exhibit lower sag and slump velocities. In general, therefore, a Newtonian or a shear-thinning fluid will sag or slump under its own weight until its viscosity increased to the point at which V 0 is negligible. However, sagging might not occur at all, provided certain conditions are met. One of these is the existence of the yield stress. No sagging occurs if the yield stress ( σ y ) is larger than the force due to gravity, pgh . However, if the coating is thick enough (large h ), this condition may no longer be satisfied, and both sagging and slumping can occur if the film thickness is larger than h s , which is given by (2.9) Between h = 0 and h = h s , sagging occurs. The velocity can be obtained by substituting (h – h s ) for h in Equation 2.7: (2.10) s Wu 31 also found that the tendency to sag, in general, increases in the order: shear-thinning fluids < viscoplastic fluids < Newtonian fluids < shear-thickening fluids, provided that all these materials have the same zero-shear viscosity, η 0 . The significance of η 0 for viscoplastic fluids is unclear, although it is used in the equations derived by Wu. 31 For the particular case of sprayable coatings, Wu found that a shear thinning fluid with n = 0.6, without a yield stress, can exhibit good sag control while retaining adequate sprayability. 2.3.4 Leveling Leveling is the critical step to achieve a smooth and uniform coating. During the application of coatings, imperfections such as waves or furrows usually appear on the surface. For the coating to be acceptable, these imperfections must disappear before the wet coating (fluid) solidifies. Surface tension has been generally recognized as the major driving force for the flow-out in coating, and the resistance to flow is the viscosity of the coating. The result of leveling is the reduction of the surface continuous fused film. For a thin film with an idealized sinusoidal surface, as shown in Figure 2.7, an equation that relates leveling speed t v with viscosity and surface tension was given by Rhodes and Orchard 32 : (2.11) where a t and a 0 are the final and initial amplitudes, γ is the wavelength, and h is the averaged thickness of the film. This equation is valid only when γ is greater than h. From Equation 2.11 it is clear that leveling is favored by large film thickness, small wavelength, high surface tension, and low melt viscosity. However, the question of the relevant viscosity to be used in Equation 2.11 is not quite settled. Lin 18 suggests computing the stress generated by surface tension with one of several available methods. 33,34 Then, from a predetermined flow curve, obtain the viscosity at that shear stress; this may necessitate the measurement of viscosity at a very low strain rate. On the other hand, Wu proposed 31 using the zero- h g s y = σ ρ V g n n hh n s nn 0 0 1 1 1 =       + − + ρ η / ()/ () t ha a v t =       16 3 43 3 0 πγ γη ln DK4036_book.fm Page 8 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC For h > h , plug flow occurs (see Figure 2.6). tension of the film. Figure 2.7 illustrates the leveling out of a newly formed sinusoidal surface of a 2-10 Coatings Technology Handbook, Third Edition after coating, the oscillatory measurement should be preceded by shearing at a fairly high rate, corre- sponding to the method of application. 36 In such an experiment, the average amplitude of the torque/ stress wave increases with time after the cessation of a ramp shear. Although it is not easy to compute the viscosity change from the amplitude change, estimating is possible. 37 Alternatively, one can use just the amplitude of the stress for correlation purposes. Dodge 36 finds a correlation between the viscosity level after application and the extent of leveling as quantified by a special technique he developed. Another method that has been used 38 involves rolling a sphere down a coating applied to an inclined surface. The speed of the sphere can be taken as an indicator of the viscosity, after suitable calibration with Newtonian fluids. This method can be very misleading, because the flow is not viscometric, and it is not applicable to non-Newtonian fluids. A more acceptable technique is to use a simple shear, with a plate being drawn at constant velocity over a horizontal coating. 19 2.3.6 Edge and Corner Effects When a film is applied around a corner, surface tension, which tends to minimize the surface area of the Figure 2.9d, respectively. In the case of edges of coated objects, an increase in the thickness has been observed. This phenomenon is related to surface tension variation with the solvent concentration. 40 In a newly formed film, a decrease in film thickness at the edge is caused by the surface tension of the film. Consequently, the solvent evaporation is much faster at the edge of the film, because there is a larger lower surface tension than the polymer) evaporates, a higher surface tension exists at the edge, hence causing a material transport toward the edge from regions 2 to 1 (Figure 2.10b). The newly formed surface in region 2 will have a lower surface tension due to the exposure of the underlying material, FIGURE 2.8 Schematic plot of coating viscosity during application and film formation. Viscosity Drying Application “Zero-Shear” Viscosity Viscoplasticity (Infinite Viscosity) Thixotropy (+ Cooling) Viscosity during Application Time Viscosity Increase due to Decrease in Shear Rate Evaporation of Solvent (+ Polymerization) DK4036_book.fm Page 10 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC film, may cause a decrease or increase in the film thickness at the corners as shown in Figure 2.9b and surface area per unit volume of fluid near the edge (Figure 2.10a). As more solvent (which usually has a 2-12 Coatings Technology Handbook, Third Edition into a more stable one in which the material at the surface has a lower surface tension and density. Theoretical analysis 45 has established two characteristic numbers: the Raleigh number R a and the Marangoni number M a , given by (2.13) (2.14) where ρ is the liquid density, g is the gravitational constant, α is the thermal expansion coefficient, τ is the temperature gradient on the liquid surface, h is the film thickness, K is the thermal diffusivity, and T is the temperature. If the critical Marangoni number is exceeded, the cellular convective flow is formed by the surface tension gradient. As shown in Figure 2.11a, the flow is upward and downward beneath the center depression and the raised edge, respectively. But if the critical Raleigh number is exceeded, the cellular convective flow, which is caused by density gradient, is downward and upward beneath the depression and the raised edge, respectively (Figure 2.11b). In general, the density-gradient-driven flow predominates in thicker liquid layers (>4 mm), while the surface tension gradient is the controlling force for thinner films. Cratering is similar to the Bernard cell formation in many ways. Craters, which are circular depressions on a liquid surface, can be caused by the presence of a low surface tension component at the film surface. The spreading of this low surface tension component causes the bulk transfer of film materials, resulting in the formation of a crater. The flow q of material during crater formation is given by 46 (2.15) where ∆γ is the surface tension difference between the regions of high and low surface tension. The crater depth d c is given by 47 (2.16) The relationship between the cratering tendency and the concentration of surfactant was investigated by Satoh and Takano. 48 Their results indicate that craters appear whenever paints contain silicon oils (a surfactant) in an amount exceeding their solubility limits. FIGURE 2.11 Schematic illustration of the formation of the Bernard cells due to (a) the surface tension gradient and (b) the density gradient. (a) (b) R ga h K a = ρτ η 4 M hddT K a = −τγ η 2 (/) q h = 2 2 ∆γ η d gh c = 3∆γ ρ DK4036_book.fm Page 12 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC Coating Rheology 2-13 In the discussion above, high surface tension and low viscosity are required for good flow-out and leveling. But high surface tension can cause cratering, and excessively low viscosity would result in sagging and poor edge coverage. To obtain an optimal coating, the balance between surface tension and viscosity is important. Figure 2.12 illustrates coating performance as a function of surface tension and melt viscosity. Coating is a fairly complex process; achieving an optimal result calls for the consideration of many factors. Acknowledgments We are grateful to Steve Trigwell for preparing the figures. References 1. A. W. Adamson, Physical Chemistry of Surfaces, 4th ed. New York: Wiley, 1982. 2. L. Du Nouy, J. Gen. Physiol., 1, 521 (1919). 3. R. H. Dettre and R. E. Johnson, Jr., J. Colloid Interface Sci., 21, 367 (1966). 4. D. S. Ambwani and T. Fort, Jr., Surface Colloid Sci., 11, 93 (1979). 5. J. R. J. Harford and E. F. T. White, Plast. Polym., 37, 53 (1969). 6. J. Twin, Phil. Trans., 29–30, 739 (1718). 7. J. W. Strutt (Lord Rayleigh), Proc. R. Soc. London, A92, 184 (1915). 8. S. Sugden, J. Chem. Soc., 1483 (1921). 9. J. M. Andreas, E. A. Hauser, and W. B. Tucker, J. Phys. Chem., 42, 1001 (1938). 10. S. Wu, J. Polym. Sci., C34, 19 (1971). 11. R. J. Roe, J. Colloid Interface Sci., 31, 228 (1969). 12. S. Fordham, Prac. R. Soc. London., A194, 1 (1948). 13. C. E. Stauffer, J. Phys. Chem., 69, 1933 (1965). 14. J. F. Padday and A. R. Pitt, Phil. Trans. R. Soc. London, A275, 489 (1973). 15. H. H. Girault, D. J. Schiffrin, and B. D. V. Smith, J. Colloid Interface Sci., 101, 257 (1984). 16. C. Huh and R. L. Reed, J. Colloid Interface Sci., 91, 472 (1983). FIGURE 2.12 The effects of surface tension and melt viscosity on coating appearance. High Low Surface Tension Acceptable Appearance Increasingly Better Flow Sagging Poor Flow (Melt Viscosity too High) Poor Flow (Surface Tension too Low) Low High Melt Viscosity Cratering (Surface Tension too High) DK4036_book.fm Page 13 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC 2-14 Coatings Technology Handbook, Third Edition 17. Y. Rotenberg, L. Boruvka, and A. W. Neumann, J. Colloid Interface Sci., 93, 169 (1983). 18. O. C. Lin, Chemtech, January 1975, p. 15. 19. L. Kornum, Rheol. Acta., 18, 178 (1979). 20. O. C. Lin, J. Apl. Polym. Sci., 19, 199 (1975). 21. H. Freundlich and A. D. Jones, J. Phys. Chem., 4(40), 1217 (1936). 22. W. H. Bauer and E. A. Collins, in Rheology, Vol. 4, F. Eirich, Ed. New York: Academic Press, 1967, Chapter 8. 23. P. S. Roller, J. Phys. Chem., 43, 457 (1939). 24. S. Reiner and G. W. Scott Blair, in Rheology, Vol. 4, F. Eirich, Ed. New York: Academic Press, 1967, Chapter 9. 25. S. LeSota, Paint Varnish. Prod., 47, 60 (1957). 26. R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1. New York: Wiley-Interscience, 1987, p. 61. 27. S. J. Storfer, J. T. DiPiazza, and R. E. Moran, J. Coating Technol., 60, 37 (1988). 28. V. G. Nix and J. S. Dodge, J. Paint Technol., 45, 59 (1973). 29. T. C. Patton, Paint Flow and Pigment Dispersion, 2nd ed. New York: Wiley-Interscience, 1979. 30. A. G. Frederickson, Principles and Applications of Rheology. Englewood Cliffs, NJ: Prentice Hall, 1964. 31. S. Wu, J. Appl. Polym. Sci., 22, 2769 (1978). 32. J. F. Rhodes and S. E. Orchard, J. Appl. Sci. Res. A, 11, 451 (1962). 33. R. K. Waring, Rheology, 2, 307 (1931). 34. N. O. P. Smith, S. E. Orchard, and A. J. Rhind-Tutt, J. Oil Colour. Chem. Assoc., 44, 618 (1961). 35. S. Wu, J. Appl. Polym. Sci., 22, 2783 (1978). 36. J. S. Dodge, J. Paint Technol., 44, 72 (1972). 37. K. Walters and R. K. Kemp, in Polymer Systems: Deformation and Flow. R. E. Wetton and R. W. Wharlow, Eds. New York: Macmillan, 1967, p. 237. 38. A. Quach and C. M. Hansen, J. Paint Technol., 46, 592 (1974). 39. L. O. Kornum and H. K. Raaschou Nielsen, Progr. Org. Coatings, 8, 275 (1980). 40. L. Weh, Plaste Kautsch, 20, 138 (1973). 41. C. G. M. Marangoni, Nuovo Cimento, 2, 239 (1971). 42. C. M. Hansen and P. E. Pierce, Ind. Eng. Chem. Prod. Res. Dev., 12, 67 (1973). 43. C. M. Hansen and Pierce, Ind. Eng. Chem. Prod. Res. Dev., 13, 218 (1974). 44. J. N. Anand and H. J. Karma, J. Colloid Interface Sci., 31, 208 (1969). 45. J. R. A. Pearson, J. Fluid Mech., 4, 489 (1958). 46. P. Fink-Jensen, Farbe Lack, 68, 155 (1962). 47. A. V. Hersey, Phys. Ser., 2, 56, 204 (1939). 48. T. Satoh and N. Takano, Colour Mater., 47, 402 (1974). DK4036_book.fm Page 14 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC 3 -1 3 Leveling 3.1 Introduction 3- 1 3.2 Yield Value 3- 1 3.3 Leveling and Viscosity 3- 2 Thixotropy 3.4 Leveling and Surface Tension 3- 3 3.5 Leveling of Brush and Striation Marks 3- 4 References 3- 4 Bibliography 3- 4 3.1 Introduction A coating is applied to a surface by a mechanical force: by a stroke of a brush, by transfer from a roll, by removing the excess with a knife’s edge, or by other means. Most of these coating processes leave surface disturbances: a brush leaves brush marks; a reverse roll coater leaves longitudinal striations; knife coating leaves machine direction streak; roll coating leaves a rough surface, when the coating splits between the roll and the substrate; and spraying may produce a surface resembling orange peel. 3.2 Yield Value These surface disturbances may disappear before the coating is dried, or they may remain, depending on the coating properties and time elapsed between the coating application and its solidification. The surface leveling process is driven by surface tension and resisted by viscosity. Some coatings, especially thickened aqueous emulsions, may exhibit pseudoplastic flow characteristics and may have a yield value: driving force (surface tension) must be higher than the yield value. Solution coatings are usually New- Viscosity measurements at very low shear rates are required to determine the yield value. Some of the operates at shear rates of 0.6 to 24 sec –1 , is not suitable for investigating the leveling effects that appear at much lower shear rates. Shear rates experienced during various coating processes are very high, and the viscosity measurements at low shear rates might not disclose coating behavior at these high shear rates. A yield value of 0.5 dynes/cm 2 produces very fine brush marks, while a yield value of 20 dynes/cm 2 produces pronounced brush marks. The yield stress necessary to suppress sagging is estimated at 5 dynes/ D. Satas* Satas & Associates * Deceased. DK4036_book.fm Page 1 Monday, April 25, 2005 12:18 PM © 2006 by Taylor & Francis Group, LLC tonian (have no yield value) and level rather well. Hot melt coatings solidify fast and may not level shear rates experienced in various processes are shown in Table 3.2. A Brookfield viscometer, which adequately. Some typical yield values for various coatings are given in Table 3.1. minimum force required to cause the coating to flow (see Figure 3.1). For such coating to level, the [...]... cohesion are dispersion forces: Wa = 2( γ L1 γ L2 )1/ 2 However, in some liquid pairs (e.g., water and hydrocarbons), this did not hold, and they coined an “interaction parameter,” Φ, given by Φ= γ L1 + γ L2 − γ L1L2 2( γ L1 γ L2 )1/ 2 Thus, Wa = 2 ( γ L1 γ L2 )1/ 2 © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 6 Monday, April 25 , 20 05 12 :18 PM 5-6 Coatings Technology Handbook, Third Edition For water... the work of adhesion between water (L1) and n-octane (L2), we have Wa = 2( γ D1 γ D2 )1/ 2 = γ L1 − γ L1L2 L L where the superscript D stands for the dispersion energy component of the total surface energy Accepted values for the surface energies and interfacial energies are as follows: γ L1 = 72. 8 ergs/cm 2 ; γ L2 = γ D2 = 21 . 8 ergs/cm 2 ; γ L1L2 = 50.8 ergs/cm 2 L If these values are substituted into... 20 05 12 :18 PM 5-4 Coatings Technology Handbook, Third Edition P U nt = 2 1 2 r3 where r is the center-to-center distance between the dipoles If the rotational energy is less than the thermal energy of the system, then U K = Keesom potential = 2 2 2 1 1 3kTr 6 where k is Boltzmann’s constant (0.08 21 1·atm/mol deg), and T is absolute temperature (K) There may be dipole-induced dipoles, where the potential... surface energy of 21 . 8 ergs/cm2 (all of it attributed to dispersion forces), the surface energy of mercury, 484 ergs/cm2, and the interfacial energy, 375 ergs/cm2, we have D Wa = 2( γ D γ n−oct )1/ 2 = γ Hg + γ n−oct − γ ( Hg ,n−oct) Hg Wa = 2( γ D × 21 . 8 )1/ 2 = 484 + 21 . 8 − 375 Hg γ D = 19 6 .2 Hg The average γ D for a series of mercury–aliphatic hydrocarbon systems yielded 20 0 ± 7 ergs/cm2 for Hg the dispersion... interface are the dispersion forces, and the work of adhesion is given by Wa = 2( 200 × 21 . 8 )1/ 2 = 484 + 72. 8 − γ ( H g , H 2O ) from which γ ( H g , H 2O ) = 424 .7 ergs/cm 2 This compares very favorably with the measured value of 426 ergs/cm2 © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 7 Monday, April 25 , 20 05 12 :18 PM 5-7 The Theory of Adhesion The work of adhesion due to dispersion forces... similar ratios Nylon γc γc(norm) © 20 06 by Taylor & Francis Group, LLC PE PTFE 56 1. 00 31 0.55 18 .5 0.33 DK4036_book.fm Page 5 Monday, April 25 , 20 05 12 :18 PM 5-5 The Theory of Adhesion 25 0 Separation in Angstrom Units 20 0 F∝ 1 D4.07 10 0 F∝ 1 D2.94 50 20 1 10 10 0 10 00 Force Constant FIGURE 5.4 Attraction between ideally planar solids In the Lifshitz equation, the force of attraction is shown to decrease... dielectric constant as follows: 1/ eo: φ(eo): 0 1 0. 025 0.53 0 .10 0. 41 0 .25 0.37 0.50 0.35 1 0.35 Strictly speaking, the dielectric constant in this expression should be measured at electron orbital frequency, about 10 15 Hz However, if we assume handbook values of the dielectric constant at 10 6 Hz, which for nylon, polyethylene, and polytetrafluoroethylene, are 3.5, 2. 3, and 2. 0, respectively, the corresponding...DK4036_C004.fm Page 1 Thursday, May 12 , 20 05 9:39 AM 4 Structure–Property Relationships in Polymers 4 .1 Structural Parameters 4 -1 Molecular-Weight Averages • Molecular Weight Between Cross-Links • Particle Size and Particle Size Distribution 4 .2 Properties of Wet Coatings .4 -2 4.3 Properties of Dried Films 4-4 Viscosity of Polymer Solutions... polymer solutions in which there are other specific attractive forces, such as in poly(n-alkyl acrylates).7 © 20 06 by Taylor & Francis Group, LLC DK4036_book.fm Page 1 Monday, April 25 , 20 05 12 :18 PM 5 The Theory of Adhesion Carl A Dahlquist 3M Company 5 .1 Contact Angle Equilibrium 5 -1 5 .2 Forces of Attraction 5-3 5.3 Real and Ideal Adhesive Bond Strengths 5-8 References .5-9... 4 -1 © 20 06 by Taylor & Francis Group, LLC DK4036_C004.fm Page 3 Thursday, May 12 , 20 05 9:39 AM 4-3 Structure–Property Relationships in Polymers TABLE 4 .1 Critical Molecular Weight of Source Polymers Polymer Mc Polyvinyl chloride Polyethylene Polyvinyl acetate Polymethyl acrylate Polystyrene 6 ,20 0 3,500 25 ,000 24 ,000 35,000 Source: From D W Van Krevelen, Properties of Polymers, Elsevier, New York, 19 76.3 . Angstrom Units 25 0 20 0 10 0 50 20 11 0 10 0 10 00 Force Constant D 4.07 1 F∝ D 2. 94 1 F∝ W aLL LL =+−γγγ 12 12 W aLL = 2 12 12 () / γγ Φ= +−γγγ γγ LL LL LL 12 12 12 2 12 () / W aLL = 2 12 12 Φ() / γγ . value of 426 ergs/cm 2 . W aL D L D LLL == 2 12 1 12 12 () / γγ γ γ γγγγ LLL D L 12 2 72 8 21 8 2 ===.; .;ergs/cm ergs/cm 2 11 2 50 8 L = .ergs/cm 2 γ HO 2 D , W a D n D Hg n Hg n ==+− −−− 2 12 () / (, γγ. =+− = 2 218 484 21 8 375 19 6 2 12 (.) . . / γ γ Hg Hg γ Hg D W aHHO g =× =+ 2 200 21 8 484 72 8 12 2 (.) . / (, ) γ γ (, ) . HHO g 2 424 7= ergs/cm 2 DK4036_book.fm Page 6 Monday, April 25 , 20 05 12 :18